Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:392AG GHM
Order: 20
Horizontal side: 392 Vertical side: 392
Elements: 1√2, 2, 2√2, 3√2, 6, 6√2, 12, 12√2, 46, 46√2, 92, 116, 92√2, 138, 162, 116√2, 184, 138√2, 230, 254.
Code: 2547 0 392 1623 254 230 1387 254 392 1386 254 254 122 266 242 123 266 230 62 272 236 63 272 230 32 275 233 10 275 233 20 274 232 21 276 232 1162 392 116 926 0 138 1847 92 230 2303 276 0 925 0 46 1163 392 0 465 0 0 464 46 0
The properties below may precede order:side in a tiling's title:
- c = crossed. There is a tile-corner traversed by two lines. The only known crossed PPIRTS's below order 20 are 19:35AB1of4 and 19:35AB4of4.
- d = double-pentagon patterned. Every such tiling is a subdivision of an instance of the same deformable tiling by two 45-90-90-90-225 pentagons with a shared side, four triangles and two pseudotriangles. All below order 19 are degenerate in the sense that one or more sides of underlying tiles have shrunk to zero length. The non-degenerate d-tilings of order 19 are 19:221AA, 19:229AB and 19:241AA.
- e = elegant. No tile-corner is just a T-junction. Such tilings may be considered aesthetically pleasing. The only known elegant PPIRTS's below order 16 are 13:21AA, 14:26AJ, 14:35AA and 15:55AA.
- i = isomers exist which are ineligible for this catalogue. They are not included in the isomer count which follows 'of' in the tiling id.
- r = rectangular inclusion. The only known PPIRTS's below order 16 with a rectangular inclusion are 13:18AA1-4of4 and 15:44AA1-4of4.
Credit for Discovery
Just three people are credited with the discovery of Primitive Perfects:
Geoffrey H. Morley (GHM, England)
Jasper D. Skinner, II (JDS, United States)
William T. Tutte (WTT, Canada, 1917-2002) (15:44AI, 17:136AJ and 19:56AJ only)